WKB asymptotics for multipoint Virasoro conformal blocks and applications
Abstract
We study multipoint Virasoro conformal blocks on the sphere in the comb channel. We arrive at the asymptotic expression for these blocks at large intermediate dimensions, applying the WKB method for the “classical Belavin-Polyakov-Zamolodchikov equation,” which is used to study (classical) Virasoro blocks via the monodromy method. Several applications of this asymptotic are discussed, such as the possibility to generalize Zamolodchikov’s elliptic recursion and numerical evaluation of amplitudes in minimal string theory. Our expressions pass nontrivial checks, such as agreement with known exact expressions for five-point blocks in special cases and the usual series expansion of Virasoro blocks computed using Alday-Gaiotto-Tachikawa correspondence.
Fields of Study & Subjects
Quantum Mechanics and Non-Hermitian Physics
Spectral Theory in Mathematical Physics
Geometry and complex manifolds
Publication details
- Journal / source
- Physical review. D/Physical review. D.
- Publisher
- American Physical Society (APS)
- Volume
- 114
- Issue
- 4
- Publication date
- 14 July 2026
- Language
- EN